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Question -

In a ∆ABC, if a = √2, b = √3 and c = √5 show that its area is1/2 √6 sq. units.



Answer -

Given:

In a ∆ABC, a = √2, b = √3 and c = √5 

By using the formulas,

We know, cos A = (b2 + c2 –a2)/2bc

By substituting the values we get,

= [(√3)2 + (√5)2 –(√2)2] / [2 × √3 × √5]

= 3/√15

We know, Area of ∆ABC = 1/2 bc sin A

To find sin A:

Sin A = √(1 – cos2 A) [by usingtrigonometric identity]

= √(1 – (3/√15)2)

= √(1- (9/15))

= √(6/15)

Now,

Area of ∆ABC = 1/2 bc sin A

= 1/2 × √3 × √5 × √(6/15)

= 1/2 √6 sq. units

Hence proved.

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